非线性薄膜方程的差分迭代求解
ifferential and Iterative Solution of Nonlinear Membrane Equation
本文对于类似于非线性薄膜一类的非线性偏微分方程,提出一种新的算法。该法首先略去非线性部分的影响,或给予非线性部分某一初值,使非线性部分成为已知,从而将原非线性方程转化为线性方程,并按差分法或其它方法求得其线性解。再将所得线性解代入非线性部分使其成为已知,再次求得其解。这样反复迭代直至收敛,进而求得原非线性方程的非线性解。
o the nonlinear partial difference equation of membrane and the like, in this paper, a new solution is put forward. That is first to neglect the effect of the nonlinear part, or to give the nonlinear part an initial value making it known. The original nonlinear equation linearized this way is to be solved by differential method or other linear methods. The linear result found this way is put into the nonlinear part to make it known again. The linearized equation can be solved as above once more. Repeat the iteration until it converges to a satisfied result. A solution to the original nonlinear equation is obtained by the iteration process finally.
杨岳民
数学力学
非线性薄膜方程差分法迭代求解
Nonlinear Equation of Membraneifferential MethodIteration Solution
杨岳民.非线性薄膜方程的差分迭代求解[EB/OL].(2009-01-21)[2025-08-16].http://www.paper.edu.cn/releasepaper/content/200901-948.点此复制
评论